Sliding Window Algorithm for Parametric Identification of Dynamical Systems with Rectangular and Ellipsoid Parameter Uncertainty Domains

The parametric identification problem for dynamical systems with rectangular and ellipsoid parameter uncertainty domains is solved for the case in which the experimental data are given in the form of intervals. The state of the considered dynamical systems at each moment of time is a parametric set. An objective function that characterizes the degree of deviation of the parametric sets of states from experimental interval estimates is constructed in the space of parameter uncertainty domains. To minimize the objective function, a sliding window algorithm has been developed, which is related to gradient methods. It is based on an adaptive interpolation algorithm that allows one to explicitly obtain parametric sets of states of a dynamical system within a given parameter uncertainty domain (window). The efficiency and performance of the proposed algorithm are demonstrated.